Amid the furore over the leak, Cable said: "When I was business secretary there were up to nine studies that we looked at that took in all the academic evidence."

“It showed that immigration had very little impact on wages or employment. But this was suppressed by the Home Office under Theresa May, because the results were inconvenient.

“I remember it vividly. Overwhelmingly it has been the case that overseas workers have been complimentary rather than competitive to British workers.”

A spokesman for the prime minister denied the claim.

He said: "When the prime minister was the home secretary, she published a number of reports on the impact of migration and one of them was specifically on the issue of employment and wages. That was published in 2014, there was also a study published by the Migration Advisory Commission which was commissioned by the prime minister as well."

Meanwhile Lord Wallace of Saltaire, who as a Lib Dem minister in the coalition wrangled over numerous revisions to an immigration report, also weighed in.

He told PolitcsHome that the Home Office had refused to use a report on migration flows and delayed one study on the free movement of people for six months.

The prime minister has insisted low skilled immigration has a direct impact on people finding themselves “out of work or on low wages”.

The immigration paper leaked to the Guardian yesterday made clear that the free movement of people from the EU will end on the day Britain quits the bloc.

It adds that those seeking low-skilled work will have their residency limited to just two years, while those in “high-skilled occupations” will be able to stay for three to five years.

SNP MP Ian Blackford today said May must “stop dancing to the tune of her right wing backbenchers” on immigration.

Concerns were also raised by the TUC and various business groups, while the Open Britain campaign group said the British economy and public service “would be put at risk” if they were implemented.

But Ukip and Migration Watch welcomed the proposals, with the latter branding them “excellent news”.

The government refused to comment on the leak but it is understood the plan has not been signed off by ministers.

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